Vapor-liquid Coexistence Densities Research Articles

Neural Network Water Model Based on the MB-Pol Many-Body Potential.

The MB-pol many-body potential accurately predicts many properties of water, including cluster, liquid phase, and vapor-liquid equilibrium properties, but its high computational cost can make applying it in large-scale simulations quite challenging. In order to address this limitation, we developed a "deep potential" neural network (DPMD) model based on the MB-pol potential for water. We find that a DPMD model trained on mostly liquid configurations yields a good description of the bulk liquid phase but severely underpredicts vapor-liquid coexistence densities. By contrast, adding cluster configurations to the neural network training set leads to a good agreement for the vapor coexistence densities. Liquid phase densities under supercooled conditions are also represented well, even though they were not included in the training set. These results confirm that neural network models can combine accuracy and transferability if sufficient attention is given to the construction of a representative training set for the target system.

Improvements and limitations of Mie λ-6 potential for prediction of saturated and compressed liquid viscosity

Over the past decade, the Mie λ-6 (generalized Lennard-Jones) potential has grown in popularity due to its improved accuracy for predicting vapor-liquid coexistence densities and pressure compared to the traditional Lennard-Jones 12-6 potential. This manuscript explores the hypothesis that greater accuracy in characterizing the coexistence properties may lead to greater accuracy for viscosity predictions. Four united-atom force fields are considered in detail: the Transferable Potentials for Phase Equilibria (TraPPE-UA and the recently developed TraPPE-2) model of Siepmann and coworkers, the Transferable Anisotropic Mie (TAMie) model of Gross and coworkers, the fourth generation anisotropic-united-atom (AUA4) model of Ungerer and coworkers, and the model of Potoff and coworkers.Equilibrium molecular dynamics simulations are analyzed using the Green-Kubo method for viscosity characterization. Simulations are performed for linear alkanes with two to twenty-two carbons and branched alkanes with four to eight carbons. Simulation conditions follow the saturated liquid from reduced temperatures of 0.5–0.85 and along the 293 K isotherm in the dense liquid region.In general, the more accurate force fields for coexistence properties do indeed predict viscosity more accurately. For saturated liquids, both Mie-based potential models (Potoff and TAMie) provide roughly 10% accuracy for linear alkanes, while deviations are between 20 and 50% for TraPPE-UA. For branched alkanes, the performance is slightly diminished, but Potoff still provides roughly 15–20% accuracy, while the TAMie force field results in deviations of 20–40%, and TraPPE-UA has deviations of approximately 25–60%. The AUA4 deviations are 10–20% for ethane and 30–60% for 2,2-dimethylpropane, the only compounds tested with the AUA4 force field. The TraPPE-2 deviations for ethane are similar to those using the original TraPPE force field, namely, between 10 and 20%. The percent deviations for each compound and force field tend to increase with decreasing temperature, with the exception of the Potoff deviations for propane, which are nearly constant to the triple point temperature.For compressed liquids, the Mie-based potential models perform better once again than the Lennard-Jones-based force fields, but tend to over estimate the viscosity at very high densities. As the Potoff and TAMie models also tend to over estimate the pressure at high densities, a fortuitous cancellation of errors leads to predictions of viscosity with respect to pressure that are accurate to within about 10%. The comparison with experimental viscosity data is limited to pressures below 200 MPa for most normal and branched alkanes. However, accurate predictions are obtained for propane near 1000 MPa with the Potoff force field.

Vapour–liquid phase equilibrium and surface tension of fully flexible Lennard–Jones chains

ABSTRACTWe report measurements of the vapour–liquid coexistence densities and surface tension of fully flexible Lennard–Jones chain molecules ranging in length from 4 to 60 beads. We demonstrate that the surface tension for all chain lengths collapses to a single master curve when plotted according to the universal parachor correlation. We find a universal parachor exponent 3.79 ± 0.05 for conditions close to the critical point, with a deviation observed for the longest chains far below the critical point.

Corresponding states law for a generalized Lennard-Jones potential.

It was recently shown that vapor-liquid coexistence densities derived from Mie and Yukawa models collapse to define a single master curve when represented against the difference between the reduced second virial coefficient at the corresponding temperature and that at the critical point. In this work, we further test this proposal for another generalization of the Lennard-Jones pair potential. This is carried out for vapor-liquid coexistence densities, surface tension, and vapor pressure, along a temperature window set below the critical point. For this purpose, we perform molecular dynamics simulations by varying the potential softness parameter to produce from very short to intermediate attractive ranges. We observed all properties to collapse and yield master curves. Moreover, the vapor-liquid curve is found to share the exact shape of the Mie and attractive Yukawa. Furthermore, the surface tension and the logarithm of the vapor pressure are linear functions of this difference of reduced second virial coefficients.

Constant-force approach to discontinuous potentials

Aiming to approach the thermodynamical properties of hard-core systems by standard molecular dynamics simulation, we propose setting a repulsive constant-force for overlapping particles. That is, the discontinuity of the pair potential is replaced by a linear function with a large negative slope. Hence, the core-core repulsion, usually modeled with a power function of distance, yields a large force as soon as the cores slightly overlap. This leads to a quasi-hardcore behavior. The idea is tested for a triangle potential of short range. The results obtained by replica exchange molecular dynamics for several repulsive forces are contrasted with the ones obtained for the discontinuous potential and by means of replica exchange Monte Carlo. We found remarkable agreements for the vapor-liquid coexistence densities as well as for the surface tension.

The Use of Anisotropic Potentials in Modeling Water and Free Energies of Hydration.

We propose a novel, anisotropic rigid-body intermolecular potential model to predict the properties of water and the hydration free energies of neutral organic solutes. The electrostatic interactions of water and the solutes are modeled using atomic multipole moments up to hexadecapole; these are obtained from distributed multipole analysis of the quantum mechanically computed charge densities and include average polarization effects in solution. The repulsion-dispersion water-water interactions are modeled with a three-site, exp-6 model fitted to the experimental liquid water density and oxygen-oxygen radial distribution function at ambient conditions. The proposed water model reproduces well several water properties not used in its parametrization, including vapor-liquid coexistence densities, the maximum in liquid water density at atmospheric pressure, the structure of ordered ice polymorphs, and the liquid water heat capacity. The model is used to compute the hydration free energy of 10 neutral organic solutes using explicit-solvent free energy perturbation. The solute-solute repulsion-dispersion intermolecular potential is obtained from previous parametrizations on organic crystal structures. In order to calculate the free energies of hydration, water-solute repulsion-dispersion interactions are modeled using Lorenz-Berthelot combining rules. The root-mean-square error of the predicted hydration free energies is 1.5 kcal mol(-1), which is comparable to the error found using a continuum mean-field quantum mechanical approach parametrized using experimental free energy of hydration data. The results are also contrasted with explicit-solvent hydration free energies obtained with an atomic charge representation of the solute's charge density computed at the same level of theory used to compute the distributed multipoles. Replacing the multipole description of the solute's charge density with an atomic charge model changes the free energy of hydration by as much as 3 kcal mol(-1) and provides an estimate for the effect of the modeling quality of the intermolecular electrostatic forces in free energy of solvation calculations.

Force field for the atomistic simulation of the properties of hydrazine, organic hydrazine derivatives, and energetic hydrazinium ionic liquids

Abstract A force field (FF) is reported for hydrazine (N2H4) and organic hydrazine derivatives, including monomethylhydrazine, 1,1-dimethylhydrazine, monoethylhydrazine, and 2-hydroxyethylhydrazine. The FF successfully reproduces a range of equilibrium properties, including vapor–liquid coexistence densities, vapor pressures, enthalpies of vaporization, and critical properties. Several dynamic properties, including self-diffusion coefficients and rotational time constants, are reported and found to be qualitatively consistent with experimental viscosities. Using this as a basis, a FF is also developed for the protonated forms of these species, i.e., hydrazinium-based cations. Properties of 1:1 energetic salts formed by pairing these cations with the nitrate anion are computed and compared with a limited amount of experimental data. The simulations indicate that the ionic liquid (IL) 2-hydroxyethylhydrazinum nitrate (2-HEHN) has significantly slower dynamics than the other hydrazinium ILs.

Improvement in molecule exchange efficiency in Gibbs ensemble Monte Carlo: Development and implementation of the continuous fractional component move

The continuous fractional component Monte Carlo (CFC MC) move (J Chem Theory Comput, 2007, 3, 1451) is extended to the Gibbs ensemble. The algorithm is validated against conventional simulations for the Lennard Jones fluid and a flexible water model. The method is also used to compute the vapor-liquid coexistence densities of a model for SO(2). The CFC molecule exchange move relies on the gradual insertion and deletion of molecules in conjunction with a self-adapting bias potential. As a result, the method does not require the formation of spontaneous voids in the dense fluid phase to be successful, leading to molecule exchange acceptance probabilities that are nearly independent of temperature. For example, over 1% of the vapor-liquid molecule exchange moves are successful for water at 280 K, whereas advanced rotational and configurational bias methods have success rates of less than 0.03%. The CFC move can be combined with other Monte Carlo moves to enable efficient simulation of dense strongly associating fluids that are to this point infeasible to model with standard methods.

Efficient simulation of chemical potentials and phase equilibria in associating fluids: monomer/dimer insertion versus gradual particle insertion in primitive water models

Widom's test particle method for simulation of chemical potentials fails for associating (network forming) fluids. Therefore we study more sophisticated insertion methods, such as gradual particle insertion and the recent unbonded particle insertion of Tripathi and Chapman. We model strongly associating fluids by short-ranged primitive models (PMs) due to Nezbeda and co-workers. Recently, we showed that gradual insertion, in principle, is applicable to PM water. Here, we study systematically subcritical chemical potential isotherms, determine vapour–liquid coexistence densities and estimate the critical point density and temperature. For comparison we implement two variants of the Tripathi–Chapman algorithm. In the first case we use as unbonded test particles only particles which remain single molecules (monomers), when inserted and in the second case such test particles which remain as single molecules or form a two-particle cluster with an existing free molecule (monomer/dimer), when inserted. While monomer insertion improves Widom's method slightly, monomer/dimer insertion extends substantially the range of application to the subcritical temperatures studied by gradual insertion. But, for low temperatures monomer/dimer insertion requires extremely long Markov chains and significantly more computer time than gradual insertion. The Tripathi–Chapman algorithm—a direct extension of Widom's method—is much simpler than gradual insertion and therefore should be preferred at supercritical and critical conditions.

Generalized equation of state for square-well potentials of variable range

An equation of state for square-well fluids of short and long potential range λ is presented and compared with Gibbs ensemble and canonical Monte Carlo simulation data; vapour–liquid coexistence densities, vapour pressures, internal energies and contact radial distribution functions are examined. The equation is an extension of that presented in previous work for the reference monomer fluid in the SAFT-VR approach [GIL-VILLEGAS et al., 1997, J. chem. Phys., 106, 4168]. The Helmholtz free energy is written as a high-temperature expansion up to second order, where simple expressions are obtained for the mean attractive energy and the fluctuation term using the mean-value theorem and a mapping of radial distribution functions. In previous work the range of the square-well potential was limited to λ ≤ 1.8. In this work we show that the phase behaviour of such a fluid is far from the expected long-range limits given by the mean-field and van der Waals approximations. We extend the applicability of the equation of state to ranges up to λ = 3, and show that, in this case, the phase behaviour of the fluid is essentially that of a fluid of infinite potential range (van der Waals limit). At short ranges (λ < 1.8) the calculated coexistence is virtually identical to that of the previous approach, hence ensuring that its application within a SAFT-VR framework is consistent with previous work. The extension of the approach to longer ranges is of interest in the context of modelling of polar fluids, and in the implementation of cross-over approaches to treat the critical region.

Renormalization group theory for fluids including critical region. I. Pure fluids

Abstract Based on White’s renormalization group (RG) theory and the statistical associating fluid theory, a new equation of state (EOS) is derived, which can be used for a variety of fluids, including non-polar, polar and associating chain fluids both inside and outside the critical region. The new EOS, with the advantage of not introducing any additional adjustable parameter to the RG transform for real fluids, yields satisfactory critical exponent, vapor–liquid coexistence densities and vapor pressures, pVT isotherms, and isobaric specific heats for pure fluids. Especially, much better results are obtained than the original EOS in the nearest vicinity of the critical point.

Monte Carlo simulation of vapor–liquid binodal of water

Gibbs ensemble Monte Carlo simulations were carried out to calculate the vapor–liquid coexistence densities (binodal curves) for two potential models of water, five-site transferable interaction potential (TIP5P) and four-site Dang–Chang potential. Both models were devised to improve a widely used water model—the four-site TIP4P model of water. Compared with the critical temperature of the TIP4P model (579 K), we found that the critical temperature of the TIP5P model (546 K) deviates further from experimental value (647 K). That of the Dang–Chang model (590 K), however, is in better agreement with the experiments.

Effective potential approach to bulk thermodynamic properties and surface tension of molecular fluids: II. Binary mixtures of n-alkanes and miscible gas

A representation of alkanes and alkane/gas mixtures is proposed in terms of simple fluids interacting through pairwise square well potentials parameterised by the range of attractive forces. Using the model, vapour–liquid equilibria and interfacial tension (IFT) are studied both for pure alkane fluids (C4, C5, C6, C8, C10 and C14) and their high pressure binary mixtures formed with methane, nitrogen or carbon dioxide. Potential parameters for the isolated components are first determined from the critical parameters, Pitzer’s acentric factor and one surface tension datum at a chosen temperature. Cross-term interactions between species are obtained from modified Lorentz–Berthelot rules which provide good fits to the vapour–liquid coexistence densities as functions of mixture composition. At a general state point, the interfacial tension is predicted using generalised van der Waals (gvdW) theory, which is a mean field free energy density functional theory. This semiempirical procedure typically produces very satisfactory agreement with experimental interfacial tension data.

Liquid vapor equilibria for an ab initio model for water

The vapor–liquid coexistence densities for water near the critical point were determined using a polarizable ab initio based model and grand canonical Monte Carlo simulations combined with the histogram reweighting technique. The predictions of the model used, which is found to give good agreement with experimental data at ambient conditions, are far below the experimental critical temperature and density. The saturation pressure is also overestimated. The source of this discrepancy may be related to the high pressure that the model exhibits even for liquid water. Since there is no fitting to experimental data, it is possible to refine the potential in a systematic way. In particular, an improvement in the sampling of the ab initio calculation for the repulsive part of the intermolecular potential is suggested in order to obtain better agreement with experiment at high temperatures and pressures.

Group contribution multifluid lattice theory for simultaneous predictions of thermodynamic properties of pure fluids and mixtures

A unified group contribution (GC) lattice equation of state (EOS) was formulated based on the multifluid approximation of the nonrandom lattice fluid theory. The GC-EOS requires segment size and interaction energy parameter from functional group characteristics. The unique feature of the approach is that a single set of group parameters are used for both pure fluids and mixtures. The approach was found to be quantitatively applicable for predicting thermodynamic properties of real pure fluids and mixtures. Its potential utility was demonstrated for vapor pressures, vapor–liquid coexistence densities of pure fluids and phase equilibrium properties of mixtures including polymeric solutions.

Vapor–liquid equilibria and heat effects of hydrogen fluoride from molecular simulation

The vapor–liquid coexistence densities, vapor pressure, and heat of vaporization of hydrogen fluoride (HF) is calculated via Monte Carlo simulation from three intermolecular potential models that are found in the literature. The first is a pure pair potential based solely on ab initio data, the second is a semi-empirical pair potential which uses an ab initio derived surface fitted with dimer spectroscopic data, and the third is an effective pair potential that was fit to experimental data for the condensed phase. As expected, the effective potential reproduces the saturated liquid densities more accurately than the others do, while all the potential models predict the wrong slope and curvature in the vapor pressure curve. The inability to reproduce the vapor pressure dependence on temperature is connected to the models’ poor prediction of the heat of vaporization at temperatures below 400 K. A biasing algorithm is introduced to study the superheated-vapor heat capacity, density, association number, and oligomer distribution along three low-pressure isobars using both the semi-empirical and effective pair potentials. It is found that both these potential models do predict a peak in the heat capacity, however, they are at cooler temperatures and only about half the magnitude relative to the experiment. When comparing the potential models to each other, it is found that the semi-empirical pair potential predicts the onset of near-ideal gas conditions at about 30 K cooler than the effective pair potential. Additionally, the percentage of ring oligomers predicted by both models is considerable at all but the highest temperatures. Both models also agree that the monomer and cyclic tetramer are the two most important species at the nonideal states.

Phase coexistence properties of polarizable water models

Vapour–liquid coexistence densities near the critical point are reported for polarizable water models, determined by a series of grand canonical Monte Carlo simulations with the histogram reweighting method. Previously proposed point charge models rescaled to match the experimental permanent dipole moment in the gas phase were used. Isotropic polarizability was added to account for three-body and higher order interactions in dense phases. The coexistence density, vapour pressure and heat of vaporization of the models were calculated. The models used in this study, including a recently introduced polarizable model that gives good agreement with the experimental structure, do not give quantitative agreement with the experimental coexistence properties. The potential parameters of the models were varied in an attempt to improve agreement with experimental values for the coexistence properties.

Experimental method for obtaining critical densities of binary mixtures: application to ethane + n-butane

Van Poolen L.J., Niesen V.G. and Rainwater J.C., 1991. Experimental method for obtaining critical densities of binary mixtures: application to ethane + n-butane. Fluid Phase Equilibria, 66: 161-185. According to the experimental and analytical procedure proposed by Van Poolen and Rainwater, rectilinear diameters based on measured vapor-liquid coexistence densities along a path of constant overall density and composition have been determined and used to obtain critical densities of the binary mixture ethane+ n-butane. Seven experimental runs for the mixture were made at compositions ranging from, 21.65 to 80.75 mol% ethane. The procedure has been explored as a new way to determine critical densities of mixtures. Results are compared with densities generated from a modified Leung-Griffiths correlation of the extensive vapor-liquid equilibrium data of Kay. The critical densities obtained are in agreement with the correlation within the overall uncertainty of the method, thereby verifying the proposed technique.